78.1.7 problem 1.g

Internal problem ID [20933]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 1, First order ODEs. Problems section 1.5
Problem number : 1.g
Date solved : Thursday, October 02, 2025 at 06:49:30 PM
CAS classification : [_separable]

\begin{align*} s^{\prime }+2 s&=s t^{2} \end{align*}

With initial conditions

\begin{align*} s \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 13

ode:=diff(s(t),t)+2*s(t) = s(t)*t^2; 
ic:=[s(0) = 1]; 
dsolve([ode,op(ic)],s(t), singsol=all);
 

\[ s = {\mathrm e}^{\frac {t \left (t^{2}-6\right )}{3}} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 20

ode=D[s[t],t]+2*s[t]==s[t]+t^2; 
ic={s[0]==1}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to t^2-2 t-e^{-t}+2 \end{align*}

✓ Sympy. Time used: 0.199 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(-t**2*s(t) + 2*s(t) + Derivative(s(t), t),0) 
ics = {s(0): 1} 
dsolve(ode,func=s(t),ics=ics)
 

\[ s{\left (t \right )} = e^{t \left (\frac {t^{2}}{3} - 2\right )} \]